 reserve i,j,n,k,l for Nat;
 reserve T,S,X,Y,Z for Subset of MC-wff;
 reserve p,q,r,t,F,H,G for Element of MC-wff;
 reserve s,U,V for MC-formula;
reserve f,g for FinSequence of [:MC-wff,Proof_Step_Kinds_IPC:];
 reserve X,T for Subset of MC-wff;
 reserve F,G,H,p,q,r,t for Element of MC-wff;
 reserve s,h for MC-formula;
 reserve f for FinSequence of [:MC-wff,Proof_Step_Kinds_IPC:];
 reserve i,j for Element of NAT;
 reserve F1,F2,F3,F4,F5,F6,F7,F8,F9,F10,G for MC-formula;
 reserve x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x for Element of MC-wff;
reserve x1,x2,x3,x4,x5,x6,x7,x8,x9,x10 for object;

theorem Th94:
  |-_IPC q => (p => (((p '&' q) => FALSUM) => FALSUM))
proof
    (p '&' q) => FALSUM in {(p '&' q) => FALSUM,p,q} by ENUMSET1:def 1; then
A1: {(p '&' q) => FALSUM,p,q} |-_IPC (p '&' q) => FALSUM by Th67;
    p in {(p '&' q) => FALSUM,p,q} by ENUMSET1:def 1; then
A2: {(p '&' q) => FALSUM,p,q} |-_IPC p by Th67;
    q in {(p '&' q) => FALSUM,p,q} by ENUMSET1:def 1; then
A3: {(p '&' q) => FALSUM,p,q} |-_IPC q by Th67;
A04: |-_IPC p => (q => (p '&' q)) by Th22;
   {}(MC-wff) c= {(p '&' q) => FALSUM,p,q}; then
   {(p '&' q) => FALSUM,p,q} |-_IPC p => (q => (p '&' q))
       by A04,Th66; then
   {(p '&' q) => FALSUM,p,q} |-_IPC q => (p '&' q) by A2,Th27;
      then
   {(p '&' q) => FALSUM,p,q} |-_IPC p '&' q by A3,Th27; then
   {(p '&' q) => FALSUM,p,q} |-_IPC FALSUM by A1,Th27; then
  {p,q} |-_IPC ((p '&' q) => FALSUM) => FALSUM by Th56; then
  {q} |-_IPC p => (((p '&' q) => FALSUM) => FALSUM) by Th55;
  hence thesis by Th54;
end;
